Diameter

Radius

Circumference of a circle =

r

D

2or

Area of a circle =

r2

Chord

Tangent

(minor) Segment

(major) Segment

Sector

Angles in the same segment are equal

x

x

x

2a

a

Angles held up by the diameter are called “Angles in the semi-circle” and are all 900

. .

The angle in a semicircle is 90°

Isosceles triangles are formed by two radii

.Radius

Tangent

Tangent and Radius meet at 90°

90°

. Chord

Any chord bisector is a diameter

680

.c

a

b= 1120 opposite angle of a cyclic quadrilateral

Opposite angles in cyclic quadrilateral add up to 1800

(supplementary)

Adjacent angles in cyclic trapezium are equal - angles subtended by an arc. Only true if trapezium.

770

.O

a

fe

c

b

d

Find the missing angles a, b, c, d, e and f

420

770

.O

= 420 angle in the same segment

f

e

c

b

d

a

= 420 angle in the same segment

= 1030 opposite angle of a cyclic quadrilateral

= 1030 interior angle= 770 adjacent angle of a cyclic trapezium

420f = 840 angle at the centre is twice the angle at the circumference

f = 840 angle at the centre is twice the angle at the circumference

. .

.1350 870

ab

.

For the following circles, where O is the centre of the circle, find the missing angles

.e

480 470

f

g390

1100

580i k

h

j

920

lm

d

c

o oo

oo

. .

.1350 870

a =930

b =450

.

For the following circles, where O is the centre of the circle, find the missing angles

.

480 470

390

1100

580920

d = 900

c= 900e = 960

f = 390

310

g = 310

i=900k=320

j=320

h=1220

l=460

m=460

b

c

de

f

g

h

a

ij

k l

m

o o o

oo

m

m

The angle between chord and tangent

The angle in the opposite segment

The angle between a chord and a tangent = the angle in the opposite segment

n

n

Two tangents drawn from an outside point are always equal in lengthalways equal in length, so creating an isosceles situation with two two congruent right-angled trianglescongruent right-angled triangles

Two tangents drawn from an outside point are always equal

in length, so creating an isosceles situation with two

congruent right-angled triangles

m

m

The angle between chord and tangent

The angle in the opposite segment The angle between a

chord and a tangent = the angle in the opposite

segment

A

O

C E

B

D

850

Find each of the following angles

OBE BOD BED BCD CAB

250

900

1700 100

950250

600

Angle between tangent and radius is a right angle

In kite BEDO, BED = 360-known angles 900 + 1700 + 900 =100Opposite angles of a cyclic

quad are supplementary

The angle between a chord and a tangent = the angle in the

opposite segment

Angle at the centre is twice the angle at the circumference